Edit: I should note I've also mixed up my terms a bit - I have meant to achieve better Z-culling -(removing faces that are occluded by other faces in the scene) rather than backface culling, which is removing faces whose normals face away from the camera...
Mark,
You're right that camera clipping shouldn't have anything to do with this problem, but it did help to "calm" the effect a little bit. For example, the darker gray slab with the yellow edges is an asphalt road with a subbase (the yellow). Before I turned on camera clipping, the subbbase faces fought with the asphalt faces, although there's substantial (several inches) of difference in their heights. So, when I saw how camera clipping cleaned up that issue, I presumed Z-culling was also taking place, and not just a simple cutting of the volume between a front and rear plane...
Anyway, I suspect it's probably because we're running low-spec video cards, so obviously anything that reduces the total visible volume would probably help issues like that.
In the end, shutting off the shape's levels fixed the problem. Thanks for the tip.